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| <div class="section" lang="en"> |
| <div class="titlepage"><div><div><h3 class="title"> |
| <a name="boost_icl.concepts.map_traits"></a><a class="link" href="map_traits.html" title="Map Traits">Map Traits</a> |
| </h3></div></div></div> |
| <p> |
| Icl maps differ in their behavior dependent on how they handle <a href="http://en.wikipedia.org/wiki/Identity_element" target="_top"><span class="emphasis"><em><span class="bold"><strong>identity elements</strong></span></em></span></a> of the associated |
| type <code class="computeroutput"><span class="identifier">CodomainT</span></code>. |
| </p> |
| <a name="boost_icl.concepts.map_traits.remarks_on_identity_elements"></a><h5> |
| <a name="id1075200"></a> |
| <a class="link" href="map_traits.html#boost_icl.concepts.map_traits.remarks_on_identity_elements">Remarks |
| on Identity Elements</a> |
| </h5> |
| <p> |
| In the pseudo code snippets below <code class="computeroutput"><span class="number">0</span></code> |
| will be used to denote <a href="http://en.wikipedia.org/wiki/Identity_element" target="_top"><code class="computeroutput"><span class="identifier">identity</span> <span class="identifier">elements</span></code></a>, |
| which can be different objects like <code class="computeroutput"><span class="keyword">const</span> |
| <span class="keyword">double</span> <span class="number">0.0</span></code>, |
| empty sets, empty strings, null-vectors etc. dependent of the instance type |
| for parameter <code class="computeroutput"><span class="identifier">CodomainT</span></code>. |
| The existence of an <span class="emphasis"><em><span class="bold"><strong>identity element</strong></span></em></span> |
| wrt. an <code class="computeroutput"><span class="keyword">operator</span><span class="special">+=</span></code> |
| is a requirement for template type <code class="computeroutput"><span class="identifier">CodomainT</span></code>. |
| </p> |
| <div class="informaltable"><table class="table"> |
| <colgroup> |
| <col> |
| <col> |
| <col> |
| </colgroup> |
| <thead><tr> |
| <th> |
| <p> |
| type |
| </p> |
| </th> |
| <th> |
| <p> |
| operation |
| </p> |
| </th> |
| <th> |
| <p> |
| identity element |
| </p> |
| </th> |
| </tr></thead> |
| <tbody> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="keyword">int</span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| addition |
| </p> |
| </td> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="number">0</span></code> |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="identifier">string</span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| concatenation |
| </p> |
| </td> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="string">""</span></code> |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="identifier">set</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| union |
| </p> |
| </td> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="special">{}</span></code> |
| </p> |
| </td> |
| </tr> |
| </tbody> |
| </table></div> |
| <p> |
| In these cases the <code class="computeroutput"><span class="identifier">identity</span> <span class="identifier">element</span></code> value is delivered by the default |
| constructor of the maps <code class="computeroutput"><span class="identifier">CodomainT</span></code> |
| type. But there are well known exceptions like e.g. numeric multiplication: |
| </p> |
| <div class="informaltable"><table class="table"> |
| <colgroup> |
| <col> |
| <col> |
| <col> |
| </colgroup> |
| <thead><tr> |
| <th> |
| <p> |
| type |
| </p> |
| </th> |
| <th> |
| <p> |
| operation |
| </p> |
| </th> |
| <th> |
| <p> |
| identity element |
| </p> |
| </th> |
| </tr></thead> |
| <tbody><tr> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="keyword">int</span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| multiplication |
| </p> |
| </td> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="number">1</span></code> |
| </p> |
| </td> |
| </tr></tbody> |
| </table></div> |
| <p> |
| Therefore icl functors, that serve as <code class="computeroutput"><span class="identifier">Combiner</span></code> |
| parameters of icl Maps implement a static function <code class="computeroutput"><span class="identifier">identity_element</span><span class="special">()</span></code> to make sure that the correct <code class="computeroutput"><span class="identifier">identity_element</span><span class="special">()</span></code> |
| is used in the implementation of <span class="emphasis"><em>aggregate on overlap</em></span>. |
| |
| </p> |
| <pre class="programlisting"><span class="identifier">inplace_times</span><span class="special"><</span><span class="keyword">int</span><span class="special">>::</span><span class="identifier">identity_element</span><span class="special">()</span> <span class="special">==</span> <span class="number">1</span> |
| <span class="comment">// or more general |
| </span><span class="identifier">inplace_times</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">identity_element</span><span class="special">()</span> <span class="special">==</span> <span class="identifier">unit_element</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">value</span><span class="special">()</span> |
| </pre> |
| <p> |
| </p> |
| <a name="boost_icl.concepts.map_traits.definedness_and_storage_of_identity_elements"></a><h5> |
| <a name="id1075678"></a> |
| <a class="link" href="map_traits.html#boost_icl.concepts.map_traits.definedness_and_storage_of_identity_elements">Definedness |
| and Storage of Identity Elements</a> |
| </h5> |
| <p> |
| There are two <span class="emphasis"><em>properties</em></span> or <span class="emphasis"><em>traits</em></span> |
| of icl maps that can be chosen by a template parameter <code class="computeroutput"><span class="identifier">Traits</span></code>. |
| The <span class="emphasis"><em><span class="bold"><strong>first trait</strong></span></em></span> relates |
| to the <span class="emphasis"><em><span class="bold"><strong>definedness</strong></span></em></span> |
| of the map. Icl maps can be <span class="bold"><strong>partial</strong></span> or |
| <span class="bold"><strong>total</strong></span> on the set of values given by domain |
| type <code class="computeroutput"><span class="identifier">DomainT</span></code>. |
| </p> |
| <div class="itemizedlist"><ul type="disc"> |
| <li> |
| A <span class="emphasis"><em><span class="bold"><strong>partial</strong></span></em></span> map is |
| only defined on those key elements that have been inserted into the Map. |
| This is usually expected and so <span class="emphasis"><em><span class="bold"><strong>partial |
| definedness</strong></span></em></span> is the default. |
| </li> |
| <li> |
| Alternatively an icl Map can be <span class="emphasis"><em><span class="bold"><strong>total</strong></span></em></span>. |
| It is then considered to contain a <span class="emphasis"><em><span class="bold"><strong>neutral |
| value</strong></span></em></span> for all key values that are not stored in the |
| map. |
| </li> |
| </ul></div> |
| <p> |
| The <span class="emphasis"><em><span class="bold"><strong>second trait</strong></span></em></span> is |
| related to the representation of <code class="computeroutput"><span class="identifier">identity</span> |
| <span class="identifier">elements</span></code> in the map. An icl map |
| can be a <span class="emphasis"><em><span class="bold"><strong>identity absorber</strong></span></em></span> |
| or a <span class="emphasis"><em><span class="bold"><strong>identity enricher</strong></span></em></span>. |
| </p> |
| <div class="itemizedlist"><ul type="disc"> |
| <li> |
| A <span class="emphasis"><em><span class="bold"><strong>identity absorber</strong></span></em></span> |
| never stores value pairs <code class="computeroutput"><span class="special">(</span><span class="identifier">k</span><span class="special">,</span><span class="number">0</span><span class="special">)</span></code> that carry identity elements. |
| </li> |
| <li> |
| A <span class="emphasis"><em><span class="bold"><strong>identity enricher</strong></span></em></span> |
| stores value pairs <code class="computeroutput"><span class="special">(</span><span class="identifier">k</span><span class="special">,</span><span class="number">0</span><span class="special">)</span></code>. |
| </li> |
| </ul></div> |
| <p> |
| For the template parameter <code class="computeroutput"><span class="identifier">Traits</span></code> |
| of icl Maps we have the following four values. |
| </p> |
| <div class="informaltable"><table class="table"> |
| <colgroup> |
| <col> |
| <col> |
| <col> |
| </colgroup> |
| <thead><tr> |
| <th> |
| <p> |
| </p> |
| </th> |
| <th> |
| <p> |
| identity absorber |
| </p> |
| </th> |
| <th> |
| <p> |
| identity enricher |
| </p> |
| </th> |
| </tr></thead> |
| <tbody> |
| <tr> |
| <td> |
| <p> |
| partial |
| </p> |
| </td> |
| <td> |
| <p> |
| partial_absorber <span class="emphasis"><em>(default)</em></span> |
| </p> |
| </td> |
| <td> |
| <p> |
| partial_enricher |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| total |
| </p> |
| </td> |
| <td> |
| <p> |
| total_absorber |
| </p> |
| </td> |
| <td> |
| <p> |
| total_enricher |
| </p> |
| </td> |
| </tr> |
| </tbody> |
| </table></div> |
| <a name="boost_icl.concepts.map_traits.map_traits_motivated"></a><h5> |
| <a name="id1077612"></a> |
| <a class="link" href="map_traits.html#boost_icl.concepts.map_traits.map_traits_motivated">Map Traits |
| motivated</a> |
| </h5> |
| <p> |
| Map traits are a late extension to the <span class="bold"><strong>icl</strong></span>. |
| Interval maps have been used for a couple of years in a variety of applications |
| at Cortex Software GmbH with an implementation that resembled the default |
| trait. Only the deeper analysis of the icl's <span class="emphasis"><em><span class="bold"><strong>aggregating |
| Map's concept</strong></span></em></span> in the course of preparation of the library |
| for boost led to the introduction of map Traits. |
| </p> |
| <a name="boost_icl.concepts.map_traits.add_subtract_antinomy_in_aggregating_maps"></a><h6> |
| <a name="id1077639"></a> |
| <a class="link" href="map_traits.html#boost_icl.concepts.map_traits.add_subtract_antinomy_in_aggregating_maps">Add-Subtract |
| Antinomy in Aggregating Maps</a> |
| </h6> |
| <p> |
| Constitutional for the absorber/enricher propery is a little antinomy. |
| </p> |
| <p> |
| We can insert value pairs to the map by <span class="emphasis"><em><span class="bold"><strong>adding</strong></span></em></span> |
| them to the map via operations <code class="computeroutput"><span class="identifier">add</span><span class="special">,</span> <span class="special">+=</span></code> or <code class="computeroutput"><span class="special">+</span></code>: |
| </p> |
| <pre class="programlisting"><span class="special">{}</span> <span class="special">+</span> <span class="special">{(</span><span class="identifier">k</span><span class="special">,</span><span class="number">1</span><span class="special">)}</span> <span class="special">==</span> <span class="special">{(</span><span class="identifier">k</span><span class="special">,</span><span class="number">1</span><span class="special">)}</span> <span class="comment">// addition</span></pre> |
| <p> |
| </p> |
| <p> |
| Further addition on common keys triggers aggregation: |
| </p> |
| <pre class="programlisting"><span class="special">{(</span><span class="identifier">k</span><span class="special">,</span><span class="number">1</span><span class="special">)}</span> <span class="special">+</span> <span class="special">{(</span><span class="identifier">k</span><span class="special">,</span><span class="number">1</span><span class="special">)}</span> <span class="special">==</span> <span class="special">{(</span><span class="identifier">k</span><span class="special">,</span><span class="number">2</span><span class="special">)}</span> <span class="comment">// aggregation for common key k</span></pre> |
| <p> |
| </p> |
| <p> |
| A subtraction of existing pairs |
| </p> |
| <pre class="programlisting"><span class="special">{(</span><span class="identifier">k</span><span class="special">,</span><span class="number">2</span><span class="special">)}</span> <span class="special">-</span> <span class="special">{(</span><span class="identifier">k</span><span class="special">,</span><span class="number">2</span><span class="special">)}</span> <span class="special">==</span> <span class="special">{(</span><span class="identifier">k</span><span class="special">,</span><span class="number">0</span><span class="special">)}</span> <span class="comment">// aggregation for common key k</span></pre> |
| <p> |
| yields value pairs that are associated with 0-values or <code class="computeroutput"><span class="identifier">identity</span> |
| <span class="identifier">elements</span></code>. |
| </p> |
| <p> |
| So once a value pair is created for a key <code class="computeroutput"><span class="identifier">k</span></code> |
| it can not be removed from the map via subtraction (<code class="computeroutput"><span class="identifier">subtract</span><span class="special">,</span> <span class="special">-=</span></code> or <code class="computeroutput"><span class="special">-</span></code>). |
| </p> |
| <p> |
| The very basic fact on sets, that we can remove what we have previously added |
| |
| </p> |
| <pre class="programlisting"><span class="identifier">x</span> <span class="special">-</span> <span class="identifier">x</span> <span class="special">=</span> <span class="special">{}</span></pre> |
| <p> |
| does not apply. |
| </p> |
| <p> |
| This is the motivation for the <span class="emphasis"><em><span class="bold"><strong>identity absorber</strong></span></em></span> |
| Trait. A identity absorber map handles value pairs that carry identity elements |
| as <span class="emphasis"><em><span class="bold"><strong>non-existent</strong></span></em></span>, which |
| saves the law: |
| </p> |
| <pre class="programlisting"><span class="identifier">x</span> <span class="special">-</span> <span class="identifier">x</span> <span class="special">=</span> <span class="special">{}</span></pre> |
| <p> |
| </p> |
| <p> |
| Yet this introduces a new problem: With such a <span class="emphasis"><em>identity absorber</em></span> |
| we are <span class="emphasis"><em>by definition</em></span> unable to store a value <code class="computeroutput"><span class="special">(</span><span class="identifier">k</span><span class="special">,</span><span class="number">0</span><span class="special">)</span></code> in the map. |
| This may be unfavorable because it is not inline with the behavior of stl::maps |
| and this is not necessarily expected by clients of the library. |
| </p> |
| <p> |
| The solution to the problem is the introduction of the identity enricher |
| Trait, so the user can choose a map variant according to her needs. |
| </p> |
| <a name="boost_icl.concepts.map_traits.partial_and_total_maps"></a><h6> |
| <a name="id1078061"></a> |
| <a class="link" href="map_traits.html#boost_icl.concepts.map_traits.partial_and_total_maps">Partial |
| and Total Maps</a> |
| </h6> |
| <p> |
| The idea of a identity absorbing map is, that an <span class="emphasis"><em><span class="bold"><strong>associated |
| identity element</strong></span></em></span> value of a pair <code class="computeroutput"><span class="special">(</span><span class="identifier">k</span><span class="special">,</span><span class="number">0</span><span class="special">)</span></code> <span class="emphasis"><em><span class="bold"><strong>codes non-existence</strong></span></em></span> |
| for it's key <code class="computeroutput"><span class="identifier">k</span></code>. So the pair |
| <code class="computeroutput"><span class="special">(</span><span class="identifier">k</span><span class="special">,</span><span class="number">0</span><span class="special">)</span></code> |
| immediately tunnels from a map where it may emerge into the realm of non |
| existence. |
| </p> |
| <pre class="programlisting"><span class="special">{(</span><span class="identifier">k</span><span class="special">,</span><span class="number">0</span><span class="special">)}</span> <span class="special">==</span> <span class="special">{}</span></pre> |
| <p> |
| </p> |
| <p> |
| If identity elements do not code <span class="emphasis"><em><span class="bold"><strong>non-existence</strong></span></em></span> |
| but <span class="emphasis"><em><span class="bold"><strong>existence with null quantification</strong></span></em></span>, |
| we can also think of a map that has an associated identity element <span class="emphasis"><em><span class="bold"><strong>for every</strong></span></em></span> key <code class="computeroutput"><span class="identifier">k</span></code> |
| that has no associated value different from 0. So in contrast to modelling |
| <span class="bold"><strong>all</strong></span> neutral value pairs <code class="computeroutput"><span class="special">(</span><span class="identifier">k</span><span class="special">,</span><span class="number">0</span><span class="special">)</span></code> as being <span class="emphasis"><em><span class="bold"><strong>non-existent</strong></span></em></span> |
| we can model <span class="bold"><strong>all</strong></span> neutral value pairs <code class="computeroutput"><span class="special">(</span><span class="identifier">k</span><span class="special">,</span><span class="number">0</span><span class="special">)</span></code> as being |
| <span class="emphasis"><em><span class="bold"><strong>implicitly existent</strong></span></em></span>. |
| </p> |
| <p> |
| A map that is modelled in this way, is one large vector with a value <code class="computeroutput"><span class="identifier">v</span></code> for every key <code class="computeroutput"><span class="identifier">k</span></code> |
| of it's domain type <code class="computeroutput"><span class="identifier">DomainT</span></code>. |
| But only non-identity values are actually stored. This is the motivation |
| for the definedness-Trait on <code class="computeroutput"><span class="identifier">icl</span> |
| <span class="identifier">Maps</span></code>. |
| </p> |
| <p> |
| A <span class="emphasis"><em><span class="bold"><strong>partial</strong></span></em></span> map models |
| the intuitive view that only value pairs are existent, that are stored in |
| the map. A <span class="emphasis"><em><span class="bold"><strong>total</strong></span></em></span> map |
| exploits the possibility that all value pairs that are not stored can be |
| considered as being existent and <span class="emphasis"><em><span class="bold"><strong>quantified</strong></span></em></span> |
| with the identity element. |
| </p> |
| <a name="boost_icl.concepts.map_traits.pragmatical_aspects_of_map_traits"></a><h5> |
| <a name="id1078327"></a> |
| <a class="link" href="map_traits.html#boost_icl.concepts.map_traits.pragmatical_aspects_of_map_traits">Pragmatical |
| Aspects of Map Traits</a> |
| </h5> |
| <p> |
| From a pragmatic perspective value pairs that carry <code class="computeroutput"><span class="identifier">identity</span> |
| <span class="identifier">elements</span></code> as mapped values can often |
| be ignored. If we count, for instance, the number of overlaps of inserted |
| intervals in an <code class="computeroutput"><a class="link" href="../../boost/icl/interval_map.html" title="Class template interval_map">interval_map</a></code> |
| (see example <a class="link" href="../examples/overlap_counter.html" title="Overlap counter">overlap counter</a>), |
| most of the time, we are not interested in whether an overlap has been counted |
| <code class="computeroutput"><span class="number">0</span></code> times or has not been counted |
| at all. A identity enricher map is only needed, if we want to distinct between |
| non-existence and 0-quantification. |
| </p> |
| <p> |
| The following distinction can <span class="bold"><strong>not</strong></span> be made |
| for a <code class="computeroutput"><a class="link" href="../../boost/icl/partial_absorber.html" title="Struct partial_absorber">partial_absorber</a></code> |
| map but it can be made for an <code class="computeroutput"><a class="link" href="../../boost/icl/partial_enricher.html" title="Struct partial_enricher">partial_enricher</a></code> |
| map: |
| </p> |
| <pre class="programlisting">(k,v) does not exist in the map: Pair (k,v) has NOT been dealt with |
| (k,0) key k carries 0 : Pair (k,v) has been dealt with resulting in v=0 |
| </pre> |
| <p> |
| Sometimes this subtle distinction is needed. Then a <code class="computeroutput"><a class="link" href="../../boost/icl/partial_enricher.html" title="Struct partial_enricher">partial_enricher</a></code> |
| is the right choice. Also, If we want to give two <code class="computeroutput"><span class="identifier">icl</span><span class="special">::</span><span class="identifier">Maps</span></code> |
| a common set of keys in order to, say, iterate synchronously over both maps, |
| we need <span class="emphasis"><em>enrichers</em></span>. |
| </p> |
| </div> |
| <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> |
| <td align="left"></td> |
| <td align="right"><div class="copyright-footer">Copyright © 2007 -2010 Joachim Faulhaber<br>Copyright © 1999 -2006 Cortex Software GmbH<p> |
| Distributed under the Boost Software License, Version 1.0. (See accompanying |
| file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) |
| </p> |
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